Apparatus and methods for concentration determination using polarized light

ABSTRACT

Methods and apparatus for concentration determination using polarized light. The apparatus includes a first polarized light source having a first light source polarization axis and a second polarized light source having a second light source polarization axis generally perpendicular to the first light source polarization axis. Also, a first polarized light receiver having a first polarized light receiver polarization axis and configured to measure an intensity of light transmitted from the first light receiver polarizer and a second polarized light receiver having a second polarized light receiver polarization axis substantially perpendicular to the first light receiver polarization axis and configured to measure an intensity of light transmitted from the second light receiver polarizer, wherein the first and second light receiver polarization axes are generally +/−45 degrees relative to the first and second light source polarization axes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional patentapplication Ser. No. 60/985,003, filed 2 Nov. 2007, the entiredisclosure of which is incorporated herein by reference.

FIELD

The present disclosure relates to determining concentration of chiralmolecules in a fluid, and more particularly to an apparatus and methodfor determining concentration of chiral molecules in a fluid usingpolarized light.

BACKGROUND

There are multiple reasons to detect the concentration of a compound ina solution. One reason for detecting concentration may be to ensureproper mixing of multi-component solutions. In order to increase theshelf life of a solution, in some circumstances, the various componentsmay, for example, be kept in different chambers of a multi-chambersolution bag. The seal between the two chambers is then broken, mixingthe various components. The concentration of the mixed solution can beused as an indicator to ensure that the chambers have been properlymixed.

Additionally, online mixing of two concentrations of a solution may becarried out to achieve a desired concentration. Automatically detectingthe concentrations of solutions as well as creating and verifying adesired concentration, may allow for customized concentrations ofsolutions to be created, for example, without necessitating a premixedsolution having the desired concentration. The ability to detect theavailable concentrations and to mix different concentrations may be usedin a number of different applications.

In various additional circumstances, the concentration of glucose, achiral molecule, in a solution, or determination of the mere presence ofglucose may be desired.

SUMMARY

According to one implementation, an apparatus includes a first polarizedlight source having a first light source polarization axis and a secondpolarized light source having a second light source polarization axisgenerally perpendicular to the first light source polarization axis.Also, a first polarized light receiver having a first polarized lightreceiver polarization axis and configured to measure an intensity oflight transmitted from the first light receiver polarizer and a secondpolarized light receiver having a second polarized light receiverpolarization axis substantially perpendicular to the first lightreceiver polarization axis and configured to measure an intensity oflight transmitted from the second light receiver polarizer, wherein thefirst and second light receiver polarization axes are generally +/−45degrees relative to the first and second light source polarization axes.

According to one implementation, an apparatus includes a first lightsource polarizer having a first light source polarization axis, and asecond light source polarizer having a second light source polarizationaxis generally perpendicular to the first light source polarizationaxis. A first light receiver polarizer has a first light receiverpolarization axis, and a second light receiver polarizer has a secondlight receiver polarization axis substantially perpendicular to thefirst light receiver polarization axis, wherein the first and secondlight receiver polarization axes are generally +/−45 degrees relative tothe first and second light source polarization axes. A first lightreceiver is configured to measure an intensity of light transmitted fromthe first light receiver polarizer, and a second light receiver isconfigured to measure an intensity of light transmitted from the secondlight receiver polarizer.

One or more of the following features may be included. A first lightsource may be configured to provide light incident upon the first lightsource polarizer. The light incident upon the first light sourcepolarizer may be substantially randomly polarized. A second light sourcemay configured to provide light incident upon the second light sourcepolarizer. The light incident upon the second light source polarizer maybe substantially randomly polarized. One or more of the first lightsource and the second light source may include a laser diode.

A test region may be included, in which at least a portion of the testregion may be at least partially disposed between the first and secondlight source polarizers and the first and second light receiverpolarizers. The test region may include an at least partiallytransparent fluid passage configured to allow a fluid containing aconcentration of chiral molecules to flow through the test region. Thechiral molecules may include glucose molecules.

One or more of the first light source polarizer and the second lightsource polarizer may include an interface surface disposed at Brewster'sangle relative to an optical path between at least one of the firstlight source polarizer and the second light source polarizer and atleast one of the first light receiver polarizer and the second lightreceiver polarizer. One or more of the first light receiver polarizerand the second light receiver polarizer may include an interface surfacedisposed at Brewster's angle relative to an optical path between atleast one of the first light source polarizer and the second lightsource polarizer and at least one of the first light receiver polarizerand the second light receiver polarizer.

According to another implementation, a method includes receiving lightvia a first optical path. The first optical path includes a first lightsource polarizer having a first light source polarization axis and afirst light receiver polarizer having a first light receiverpolarization axis being generally +45 degrees relative to the firstlight source polarization axis. Light is received via a second opticalpath. The second optical path includes the first light source polarizerand a second light receiver polarizer having a second light receiverpolarization axis being generally −45 degrees relative to the firstlight source polarization axis. Light is received via a third opticalpath. The third optical path includes a second light source polarizerand the first light receiver polarizer. The second light sourcepolarizer has a second light source polarization axis being generally 90degrees relative to the first light source polarization axis. Light isreceived via a fourth optical path including the second light sourcepolarizer and the second light receiver polarizer.

One or more of the following features may be included. Receiving lightvia the first and the second optical paths may include directing lightfrom a first light source incident upon the first light sourcepolarizer. The light from the first light source may be substantiallyrandomly polarized. Receiving light via the third and the fourth opticalpaths may include directing light from a second light source incidentupon the second light source polarizer. The light from the second lightsource may be substantially randomly polarized.

An intensity of light received via the first and third optical paths maybe measured by a first light receiver. An intensity of light receivedvia the second and fourth optical paths may be measured by a secondlight receiver. The first optical path, the second optical path, thethird optical path, and the fourth optical path may include a testregion. At least a portion of the test region may be at least partiallydisposed between the first and second light source polarizers and thefirst and second light receiver polarizers. The test region may includean at least partially transparent fluid passage that may be configuredto allow a fluid containing a concentration of chiral molecules to flowthrough the test region. A polarization angle shift associated with theconcentration of chiral molecules within the test region may bedetermined, based upon, at least in part, the respective intensity oflight received via the first optical path, the second optical path, thethird optical path, and the fourth optical path.

One or more of the first light source polarizer and the second lightsource polarizer may include an interface surface disposed at Brewster'sangle relative to one or more of the first optical path, the secondoptical path, the third optical path, and the fourth optical path. Oneor more of the first light receiver polarizer and the second lightreceiver polarizer may include an interface surface disposed atBrewster's angle relative to one or more of the first optical path, thesecond optical path, the third optical path, and the fourth opticalpath.

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features andadvantages will become apparent from the description, the drawings, andthe claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically depicts an embodiment of a quad matrix polarimeter.

FIG. 2 is a flow chart of a polarization angle shift determinationprocess that may be performed utilizing the quad matrix polarimeter ofFIG. 1.

FIG. 3 is a graph representing the transfer function H_(AC) as afunction of θC−θA.

FIG. 4 diagrammatically depicts an optical path oriented at Brewster'sangle relative to an interface surface.

FIG. 5 schematically depicts an embodiment of a quad matrix polarimeterutilizing interface surfaces oriented at Brewster's angle as polarizingelements.

FIG. 5A diagrammatically depicts an embodiment of a quad matrixpolarimeter assembly according to the embodiment shown in FIG. 5.

FIG. 6 diagrammatically depicts an exemplary embodiment of a quad matrixpolarimeter.

FIG. 7 diagrammatically depicts an embodiment of a quad matrixpolarimeter assembly of FIG. 6.

FIG. 8 diagrammatically depicts an embodiment of a quad matrixpolarimeter assembly of FIG. 6.

FIG. 9 diagrammatically depicts an embodiment of a quad matrixpolarimeter assembly of FIG. 6.

FIG. 10 is an enlarged view of a light source assembly of the embodimentof the quad matrix polarimeter assembly shown in FIG. 7-9.

FIG. 11 is an enlarged view of a light receiver assembly of theembodiment of the quad matrix polarimeter assembly shown in FIG. 7-9.

FIG. 12 diagrammatically depicts an embodiment of a quad matrixpolarimeter assembly of FIG. 6.

DETAILED DISCUSSION OF EXEMPLARY EMBODIMENTS

Referring to FIG. 1, quad matrix polarimeter 10 is schematicallydepicted. Quad matrix polarimeter 10 may generally include first lightsource polarizer 12 and second light source polarizer 14. First lightsource polarizer 12 may have a first light source polarization axis(e.g., which may be generally vertically oriented in the illustratedembodiment). Second light source polarizer 14 may have a second lightsource polarization axis that may be generally perpendicular to thefirst light source polarization axis (e.g., may be generally verticallyoriented, in the illustrated embodiment).

Quad matrix polarimeter 10 may also include first light receiverpolarizer 16 and second light receiver polarizer 18. Similar to firstand second light source polarizers 12, 14, first light receiverpolarizer 16 may have a first light receiver polarization axis andsecond light receiver polarizer 18 may have a second light receiverpolarization axis that may be generally perpendicular to the first lightreceiver polarization axis. Further, the first and second light receiverpolarization axes may be generally oriented at +/−45 degrees relative tothe first and second light source polarization axes of first and secondlight source polarizers 12, 14. For example, in the illustrativeembodiment of FIG. 1, the first and second light receiver polarizationaxes may be generally oriented at 45 degrees to the vertical (orhorizontal), and may be generally perpendicular to one another. That is,the first light receiver polarization axis of first light receiverpolarizer 16 may be oriented generally at 45 degrees to the right ofvertical, and the second light receiver polarization axis of secondlight receiver polarizer 18 may be oriented generally at 45 degrees tothe left of vertical.

Although FIG. 1 schematically represents embodiments having separatelight source polarizers and light receiver polarizers, in someembodiments, the light source may be a polarized light source, i.e., apolarized light-emitting diode (“LED”), laser or other polarized lightsource, and the light receivers may be a receiver sensitive to lightalong one axis. In these embodiments, the light source polarizers andthe light receiver polarizers would not be necessary and may be removed.

Consistent with the arrangement of the polarizers (e.g., first lightsource polarizer 12, and second light source polarizer 14 beinggenerally perpendicular to one another and first light receiverpolarizer 16 and second light source polarizer 18 being generallyoriented at +/−45 degrees relative to first and second light sourcepolarizers 12, 14), the relative polarizations may be as follows (inwhich first light source polarizer 12 is designated “A”, second lightsource polarizer 14 is designated “B”, first light receiver polarizer 16is designated “C”, and second light receiver polarizer 18 is designated“D”):

Relative polarization between sources and sensors source sensor relativepolarization A C θ_(AC) = θ_(AC0) + φ_(AC), where θ_(AC0) = 45° A Dθ_(AD) = θ_(AD0) + φ_(AD), where θ_(AD0) = −45° B C θ_(BC) = θ_(BC0) +φ_(BC), where θ_(BC0) = −45° B D θ_(BD) = θ_(BD0) + φ_(BD), whereθ_(BD0) = 45°where the angles θ_(xy0) are nominal angles and the angles φ_(xy) aremanufacturing tolerance errors (e.g., φ_(AC)=θ_(C)−θ_(A)−θ_(AC0), whereθ_(C) and θ_(A) are the angles of each polarizer's axis of polarization,which may follow similarly for the other three pairs of polarizers) thathave the relation φ_(AC)−φ_(AD)−φ_(BC)+φ_(BD)=0. This can also bewritten as:

$\begin{matrix}{\phi_{Q} = {\frac{\phi_{AD} + \phi_{BC}}{2} = \frac{\phi_{BD} + \phi_{AC}}{2}}} & (1)\end{matrix}$which may be a characteristic quantity of the alignment of thepolarizers.

Quad matrix polarimeter 10 may further include first light receiver 20and second light receiver 22. First light receiver 20 may be configuredto measure an intensity of light transmitted from first light receiverpolarizer 16. Similarly, second light receiver 22 may be configured tomeasure an intensity of light transmitted from second light receiverpolarizer 18. First and second light receivers 20, 22 may be anysuitable light sensor that may measure the intensity of any lighttransmitted from first and second light receiver polarizers 16, 18,respectively. An example of a suitable light sensor may include, but isnot limited to a TSL250RD sensor manufactured by TAOS Inc. of PlanoTex., which may be sensitive to wavelengths in the 300-1000 nm rangewith maximum responsivity at a wavelength of 750 nm and goodresponsivity (e.g., 50% of maximum) in the wavelength range of 450-900nm. First and second light receivers 20, 22 may provide an output signalthat is linearly proportional to the level of light intensity received,e.g., which may be digitized by an analog-to-digital converter. In someembodiments, light receivers 20, 22 may have a relatively fast response(e.g., less than about 10 milliseconds).

First and second light sources 24, 26 may be respectively associatedwith first and second light source polarizers 12, 14. First and secondlight sources 24, 26 may respectively provide light incident upon firstand second light source polarizers 12, 14. The light from first andsecond light sources 24, 26, which may be incident upon respective firstand second light source polarizers 12, 14, may be generally randomlypolarized light. While any light source may generally be used (e.g., anincandescent light source, LED, etc.), according to an embodiment firstand second light sources 24, 26 may include a collimated light source,such as a laser diode, a non-collimated light source in conjunction withone or more collimating optical elements (e.g., lenses, reflectors,etc.), or the like.

According to one aspect, quad matrix polarimeter 10 may be used todetect polarizing mediums and/or evaluate one or more characteristics ofa polarizing medium. Accordingly, quad matrix polarimeter 10 may includetest region 28, shown in broken line. At least a portion of test region28 may be at least partially disposed between the light sourcepolarizers (e.g., first light source polarizer 12 and second lightsource polarizer 14) and the light receiver polarizers (e.g., firstlight receiver polarizer 16 and second light receiver polarizer 18). Assuch, light passing from either of the light source polarizers (e.g.,first light source polarizer 12 and/or second light source polarizer 14)to either light receiver polarizer (e.g., first light receiver polarizer16 and/or second light receiver polarizer 18) may pass through testregion 28.

Test region 28 may include fluid passage 30 configured to allow a fluidcontaining a concentration of chiral molecules (e.g., a polarizingmedium) to flow through test region 28. Fluid passage 30 may be at leastpartially transparent, e.g., to light emitted by first and/or secondlight sources 24, 26. In one embodiment, fluid passage 30 may be aportion of a dialysis apparatus (e.g., may include a portion of adialysis cassette through which a dialysate may flow). In an embodimentin which fluid passage 30 may include a portion of a dialysis apparatus,the fluid containing a concentration of chiral molecules may include aglucose solution, in which glucose may be the chiral molecule.

Referring also to FIG. 2, a method for determining the presence and/orcharacter of a polarizing medium may include receiving 50 light viafirst optical path OP1, in FIG. 1. As shown in FIG. 1, first opticalpath OP1 may include first light source polarizer 12 and first lightreceiver polarizer 16. Additionally, light may be received 52 via secondoptical path OP2, in FIG. 1. Second optical path OP2 may include firstlight source polarizer 12 and second light receiver polarizer 18.Receiving light 50, 52 via first optical path OP1 and second opticalpath OP2 may include directing 54 substantially randomly polarized lightfrom first light source 24 incident upon first light source polarizer12.

Similarly, light may be received 56 via third optical path OP3, inFIG. 1. Third optical path OP3 may include second light source polarizer14 and first light receiver polarizer 16. Additionally, light may bereceived 58 via fourth optical path OP4, in FIG. 1. Fourth optical pathOP4 may include second light source polarizer 14 and second lightreceiver polarizer 18. Receiving 56, 58 light via third optical path OP3and fourth optical path OP4 may include directing 60 substantiallyrandomly polarized light from second light source 26 incident uponsecond light source polarizer 14.

An intensity of light received 50, 56 via the first and third opticalpaths (e.g., optical paths OP1 and OP3) may be measured 62 by firstlight receiver 20. Similarly, an intensity of light received 52, 58 viathe second and fourth optical paths (e.g., optical paths OP2, OP4) maybe measured 64 by second light receiver 22. As shown in the schematicdiagram of quad matrix polarimeter 10 in FIG. 1, each of the opticalpaths (e.g., first optical path OP1, second optical path OP2, thirdoptical path OP3, and fourth optical path OP4) may pass through testregion 30 which may include a fluid containing a concentration of chiralmolecules, such as a glucose solution, in one example. As will beappreciated, the chiral molecules (e.g., glucose) may act on the lighttransmitted from each of first light source polarizer 12 and secondlight source polarizer 14 causing a polarization angle shift of thelight passing through the fluid containing the concentration of glucose.

Light transmitted from each of first light source polarizer 12 andsecond light source polarizer 14 may be incident upon both of firstlight receiver polarizer 16 and second light receiver polarizer 18 withsufficient intensity to produce an acceptable signal at both of firstlight receiver 20 and second light receiver 22. For example, if the pathlength of each of OP1, OP2, OP3, and OP4 is long enough relative to thedistance between first light source polarizer 12 and second light sourcepolarizer 14 and relative to the distance between first light receiverpolarizer 16 and second light receiver polarizer 18, the lighttransmitted from each of first light source polarizer 12 and secondlight source polarizer 14 may be incident upon both the first lightreceiver polarizer 16 and the second light receiver polarizer 18.

While not shown, in the event that the length of the optical paths isnot large enough relative to the separation between the light sourcepolarizers and the light receiver polarizers to provide equivalentoptical transfer functions among the optical paths (e.g., OP1, OP2, OP3and OP4) one or more optical mergers and/or splitters may be utilized.For example, light from the two light sources may be joined together viaan optical merger. Similarly, the joined light from the two lightsources may be separated via an optical splitter that may be used tobring the light to the two light receivers. Examples ofmergers/splitters may include, but are not limited to, a light pipe andan optical fiber bundle. Additionally, if optical mergers/splitters areemployed, care may be taken to keep the polarization unchanged. Forexample, if an optical fiber bundle is used as an opticalmerger/splitter, the physical rotation of each fiber may be controlledin order to minimize/eliminate the effect of the polarization beingchanged in an unpredictable manner.

In an embodiment in which an optical merger/splitter is not used, thelight sources may be positioned close enough to one another (althoughthe intensity of light that travels from one light source through thepolarizer associated with the other light source may be minimize, andsimilarly the light that travels to one light receiver through thepolarizer associated with the other light receiver may also beminimized) that the axes between the light sources (e.g., including thelight source polarizers) and the light receivers (including the lightreceiver polarizers) may be perpendicular to each other (e.g. the lightsources mounted beside one another, and light receivers mounted aboveone another) to keep path length geometries as symmetric as possiblebetween the four optical pathways.

The path length of the light transmitted through the glucose solutionmay vary according to design criteria and user need, as the path lengthmay represent a compromise between attenuation of the light (as the pathlength increases) and an increase in the magnitude of polarization shift(as the path length increases). Regardless of the selected path length,it may be desirable that fluid passage 30 may not be a significantpolarizer, or at least may exhibit spatially uniform polarization, suchthat the polarizing effect of fluid passage 30 may be separated from thepolarization angle shift imparted by the glucose solution. Additionally,in the example of glucose as a chiral molecule, the light emitted byfirst and second light sources 24, 26 may have a wavelength ofapproximately 505 nm, in some embodiments, but in other embodiments, thewavelength used may vary depending on the receiver used. Glucose mayexhibit a higher constant of polarization angle shift (also known as the“constant of optical rotation” or “specific rotation”) at shorterwavelengths, which may increase the magnitude of polarization angleshift for a given path length. Thus, in various embodiments, it may bedesirable to use the shortest wavelength that the system can transmitand receive.

A polarization angle shift associated with the concentration of chiralmolecules within the test region may be determined 66, based upon, atleast in part, the respective intensity of light received via firstoptical path OP1, second optical path OP2, third optical path OP3, andfourth optical path OP4 during an initial calibration and during dataacquisition in the presence of the polarizing medium (e.g., the fluidincluding a concentration of chiral molecules). For example, quad matrixpolarimeter 10 may be calibrated, e.g., by measuring 62, 64 the lightintensity from each of the optical paths (e.g., OP1, OP2, OP3, and OP4)in the absences of a fluid including a concentration of chiralmolecules. As such, the measured 62, 64 light intensity may be anintensity of the light experiencing only the polarizing effects of firstand second light source polarizers 12, 14 and first and second lightreceiver polarizers 16, 18. The intensity of light from the respectiveoptical paths (OP1, OP2, OP3, OP4) may also be measured 62, 64 when testregion 28 includes the fluid including a concentration of chiralmolecules.

The light sources (e.g., first light source 24 and second light source26) may be turned on and off (e.g., by a microprocessor and/or othersuitable controller) and the response of each light receiver (e.g.,first light receiver 20 and second light receiver 22) may be measured,giving rise to four transfer functions that may reduce and/or eliminatethe effect of ambient light. Two exemplary sampling schemes may include(wherein light transmitted via first light source 24 and first lightsource polarizer 12 is designated “A”, light transmitted via secondlight source 26 and second light source polarizer 14 is designated “B”,light received via first light receiver polarizer 16 and first lightreceiver 20 is designated “C”, and light received via second lightreceiver polarizer 18 and second light receiver 22 is designated “D”):

Sampling scheme 1 step action 1 Turn off sources A and B. Wait for apredetermined settling time. Measure signal at sensors C and D, and callthese V_(0C) and V_(0D) 2 Turn on source A and keep B off. Wait for apredeter- mined settling time. Measure signal at sensors C and D, andcall these V_(AC) and V_(AD.) 3 Turn on source B and turn A off. Waitfor a predeter- mined settling time. Measure signal at sensors C and D,and call these V_(BC) and V_(BD.)

Transfer functions may then be derived from sampling scheme 1 asfollows:H _(AC) =V _(AC) −V _(0C)H _(BC) =V _(BC) −V _(0C)H _(AD) =V _(AD) −V _(0D)H _(BD) =V _(BD) −V _(0D)  (2)

Sampling scheme 2 step action 1 Turn off sources A and B. Wait for apredetermined settling time. Measure signal at sensors C and D, and callthese V_(0C) and V_(0D) 2 Turn on source A and keep B off. Wait for apredeter- mined settling time. Measure signal at sensors C and D, andcall these V_(AC) and V_(AD.) 3 Turn on both sources. Wait for apredetermined settling time. Measure signal at sensors C and D, and callthese V_(ABC) and V_(ABD.) 4 Turn off source A but keep source B on.Wait for a predetermined settling time. Measure signal at sensors C andD, and call these V_(BC) and V_(BD.)

Transfer functions may then be derived from sampling scheme 2 asfollows:H _(AC) =V _(ABC) −V _(BC) +V _(AC) −V _(0C)H _(BC) =V _(ABC) −V _(AC) +V _(BC) −V _(0C)H _(AD) =V _(ABD) −V _(BD) +V _(AD) −V _(0D)H _(BD) =V _(ABD) −V _(AD) +V _(BD) −V _(0D)  (3)

Either sampling scheme (as well as various other sampling schemes whichwill be apparent to those having skill in the art) may be employed.Neglecting saturation effects, sampling scheme 2 may generally be moresymmetrical and may be more likely to produce measurements with lessnoise for a given measurement than sampling scheme 1. However, themeasurements V_(ABC) and V_(ABD) may have the largest magnitudes andmay, therefore, require less light for the other measurements in orderto avoid saturation.

Determining 66 the polarization angle shift imparted by the fluidincluding the concentration of chiral molecules may include, at least inpart, comparing the measured 62, 64 light intensity during calibrationof quad matrix polarimeter 10 to the measured 62, 64 light intensitywhen test region 28 includes the fluid including the concentration ofchiral molecules. The magnitude of the polarization angle shift inducedby the concentration of chiral molecules in the fluid may result in anincrease and/or decrease in the measured 62, 64 light intensity via eachof the optical paths (OP1, OP2, OP3, and OP4) compared to the measured62, 64 intensity during calibration.

Generally the transfer function for two polarizers (e.g., polarizer “A”and polarizer “C”) placed in front of each other with their polarizationaxes aligned (e.g., pointing in the same direction) may be (and whereincorresponding equations will be apparent for the various polarizers,i.e., “B” and “D”):H _(AC) =G _(A)α_(A) K _(AC)α_(C) G _(C)/2  (4)where G_(A) and G_(C) are the gains of a light source incident onpolarizer A and of a light receiver receiving light via polarizer A andpolarizer C, K_(AC) is a relative intensity related to the geometricdependencies of polarizer A and polarizer C (e.g., source A may have anonuniform luminous intensity that varies with angle, receiver C mayhave a responsivity that varies with angle, and there may be propertiesof the particular path between A and C that increases or decreasesK_(AC) e.g. reflection or refraction effects), and α_(A) and α_(C) arethe attenuations of light waves aligned with the polarization axes ofthe polarizers (if the polarizers were ideal, these factors would be1.0). The factor of ½ is due to the fact that approximately half thelight's intensity is aligned with the polarizers' polarization axeswhich is let through, and half of the light's intensity is perpendicularto the polarizer's polarization axes, which is filtered out.

As the polarizers are rotated with respect to each other, the equationmay be rewritten as:H _(AC) =G _(A)α_(A) K _(AC)α_(C) G _(C)(1+cos 2(θ_(C)−θ_(A)))/4=G_(A)α_(A) K _(AC)α_(C) G _(C) cos²(θ_(C)−θ_(A))/2  (5)where θ_(C) and θ_(A) are the physical angles of the two polarizationaxes. If θ_(C)=θ_(A) or θ_(C)=θ_(A)+180°,H_(AC)=G_(A)α_(A)K_(AC)α_(C)G_(C)/2. If θ_(C)=θ_(A)±90°, then H_(AC)=0.While real (e.g., non-ideal) polarizers attenuate, but may not perfectlyfilter out light waves perpendicular to their axis of polarization, theforegoing equation may provide a workable approximation.

Referring also to FIG. 3, the transfer function H_(AC), as a function ofθC−θA, is shown. As shown in FIG. 3, the halfway-point for the transferfunction is at ±45° (or the equivalent angles of ±135°; the effect of apolarizer may be invariant under a 180° rotation), which isapproximately the point of steepest slope.

In the case of an isotropic (e.g., does not have a preferred orientationfor light to pass, unlike polarizers that are highly anisotropic)polarization medium (e.g., in test region 28), the transfer functionequation may be rewritten as:

$\begin{matrix}\begin{matrix}{H_{AC} = {\frac{1}{4}G_{A}\alpha_{A}K_{A\; C}\alpha_{M}\alpha_{C}{G_{C}\left( {1 + {\cos\left( {{2\theta_{C}} - {2\theta_{A}} + {2\theta_{M}}} \right)}} \right)}}} \\{= {G_{AC}{R_{AC}\left( \theta_{M} \right)}}}\end{matrix} & (6)\end{matrix}$where:

$\begin{matrix}{{G_{A\; C} = {\frac{1}{2}G_{A}\alpha_{A}K_{A\; C}\alpha_{M}\alpha_{C}G_{C}}}{{R_{A\; C}\left( \theta_{M} \right)} = {\frac{1}{2}\left( {1 + {\cos\left( {{2\;\theta_{A\; C}} + {2\;\theta_{M}}} \right)}} \right)}}} & (7)\end{matrix}$and α_(M) is the medium's attenuation and θ_(M) is the polarizationtwist caused by the presence of chiral molecules. The functionR_(AC)(θ_(M)) may be the same sine wave as shown in FIG. 3, but shiftedleft or right by twice the polarization twist θ_(M).

Referring to the transfer function vs. angle curve (e.g., as shown inFIG. 3) and the slope of the curve, it may be observed that the mostsensitive orientation to small changes in polarization twist θ_(M) iswhen the two polarizers have their axes approximately 45° apart, and theleast sensitive orientation to small changes in θ_(M) is when thepolarizers are approximately parallel or perpendicular (θ_(C)−θ_(A)=0 or±90°).

In view of the foregoing, in the quad matrix (e.g., including themeasured 62, 64 intensity of optical paths OP1, OP2, OP3 and OP4), ifthe relative polarization axes of the light source polarizers (e.g.,first light source polarizer 12 and second light source polarizer 14)and of the light receiver polarizers (e.g., first light receiverpolarizer 16 and second light receiver polarizer 18) are oriented asdiscussed above, then all four transfer functions (e.g., the transferfunction corresponding to each optical path OP1, OP2, OP3, OP4) mayoperate at their most sensitive points to small changes in polarizationtwist θ_(M). For example, the two transfer functions (those dependent onθ_(AD) and θ_(BC), i.e., OP2 and OP3, which are nominally −45°) mayincrease with small positive θ_(M). In a related manner, the twotransfer functions (those dependent on θ_(AC) and θ_(BD), i.e., OP1 andOP2, which are nominally 45°) may decrease with small positive θ_(M).The symmetry between the transfer functions may add enough redundancy ofinformation so that if manufacturing tolerances cause some of thevarious gains to be unequal or the polarization axes are not quite 45°apart, the polarization twist θ_(M) may still be detected and may beinsensitive to these manufacturing tolerances.

In view of the foregoing, determining 66 the polarization angle shiftassociated with the fluid including a concentration of chiral moleculesmay include measuring H_(AC), H_(BC), H_(AD), H_(BD) at time T₀ (i.e.,when no fluid including a concentration of chiral molecules is presentwithin test region 28) as a reference point. H_(AC), H_(BC), H_(AD),H_(BD) may also be measured at time T₁ (i.e., when the fluid including aconcentration of chiral molecules is present within test region 28).Based upon, at least in part, the foregoing measurements of H_(AC),H_(BC), H_(AD), H_(BD) at T₀ and T₁, the following may be calculated:

$\begin{matrix}{{\rho_{AC} = \frac{H_{AC}\left( {T\; 1} \right)}{H_{AC}\left( {T\; 0} \right)}}{\rho_{AD} = \frac{H_{AD}\left( {T\; 1} \right)}{H_{AD}\left( {T\; 0} \right)}}{\rho_{BC} = \frac{H_{BC}\left( {T\; 1} \right)}{H_{BC}\left( {T\; 0} \right)}}{\rho_{BD} = \frac{H_{BD}\left( {T\; 1} \right)}{H_{BD}\left( {T\; 0} \right)}}} & (8)\end{matrix}$

If the system gains (e.g. light source intensity, receiver gain,attenuation, refraction/reflection effects) other than the test medium(i.e., fluid including a concentration of chiral molecules) attenuationdo not change significantly between T₀ and T₁, then the G_(AC) terms maycancel out, and we are left with:

$\begin{matrix}{{\rho_{AC} = {{{\alpha_{M}\left( T_{1} \right)}\text{/}{{\alpha_{M}\left( T_{0} \right)} \cdot {R_{AC}\left( {\theta_{M}\left( T_{1} \right)} \right)}}\text{/}{R_{AC}\left( {\theta_{M}\left( T_{0} \right)} \right)}} = {{{\alpha_{M}\left( T_{1} \right)}\text{/}{{\alpha_{M}\left( T_{0} \right)} \cdot {\left( {1 + {\cos\; 2\left( {\theta_{C} - \theta_{A} + {\theta_{M}\left( T_{1} \right)}} \right)}} \right)/{\left( {1 + {\cos\; 2\left( {\theta_{C} - \theta_{A} + {\theta_{M}\left( T_{0} \right)}} \right)}} \right).\rho_{AC}}}}} = {{\rho_{M} \cdot \left( {1 + {\cos\; 2\left( {\theta_{{AC}\; 0} + \phi_{AC} + {\theta_{M}\left( T_{1} \right)}} \right)}} \right)}\text{/}\left( {1 + {\cos\; 2\left( {\theta_{{AC}\; 0} + \phi_{AC} + {\theta_{M}\left( T_{0} \right)}} \right)}} \right)}}}}{\rho_{AC} = {\rho_{M}\frac{1 + {\cos\; 2\left( {\theta_{{AC}\; 0} + \phi_{AC} + {\theta_{M}\left( {T\; 1} \right)}} \right)}}{1 + {\cos\; 2\left( {\theta_{{AC}\; 0} + \phi_{AC} + {\theta_{M}\left( {T\; 0} \right)}} \right)}}}}} & (9) \\{{{where}\mspace{14mu}\rho_{M}} = {{\alpha_{M}\left( T_{1} \right)}\text{/}{{\alpha_{M}\left( T_{0} \right)}.}}} & (10)\end{matrix}$

For θ_(AC0)=+45°, this becomes:ρ_(AC)=ρ_(M)·(1−sin 2(φ_(AC)+θ_(M)(T ₁)))/(1−sin 2(φ_(AC)+θ_(M)(T ₀))).ρ_(AC)=ρ_(M)·(1−sin 2φ_(AC) cos²θ_(M)(T ₁)−cos 2φ_(AC) sin 2θ_(M)(T₁))/(1−sin 2φ_(AC) cos 2θ_(M)(T ₀)−cos 2φ_(AC) sin 2θ_(M)(T ₀))

If φ_(AC) and the θ_(M)'s are small, then it may be shown thatρ_(AC)≈ρ_(M)(1−(1+2φ_(AC))sin 2δ_(M))  (11)where δ_(M)=θ_(M)(T ₁)−θ_(M)(T ₀).  (12)Similarly,ρ_(AD)≈ρ_(M)(1+(1−2φ_(AD))sin 2δ_(M))  (13)ρ_(BC)≈ρ_(M)(1+(1−2φ_(BC))sin 2δ_(M))  (14)ρ_(BD)≈ρ_(M)(1−(1+2φ_(BD))sin 2δ_(M))  (15)

Given the foregoing, it may be possible to compute the following fourquantities which may help decorrelate some of the variables involved:

$\begin{matrix}\begin{matrix}{K_{1} = {\rho_{AC} + \rho_{AD} + \rho_{BC} + \rho_{BD}}} \\\left. {\approx {{4\rho_{M}} - {2\rho_{M}\sin\; 2{\delta_{M}\left( {\phi_{AC} + \phi_{AD} + \phi_{BC} + \phi_{BD}} \right)}}}} \right) \\{= {{4\rho_{M}} - {8\rho_{M}\phi_{Q}\sin\; 2\delta_{M}}}}\end{matrix} & (16) \\\begin{matrix}{K_{2} = {{- \rho_{AC}} + \rho_{AD} + \rho_{BC} - \rho_{BD}}} \\{\approx {{4\rho_{M}\sin\; 2\delta_{M}} + {2\;\sin\; 2{\delta_{M}\left( {\phi_{AC} - \phi_{AD} - \phi_{BC} + \phi_{BD}} \right)}}}} \\{= {4\rho_{M}\sin\; 2\delta_{M}}}\end{matrix} & (17) \\\left( {{{{since}\mspace{14mu}\phi_{AC}} - \phi_{AD} - \phi_{BC} + \phi_{BD}} = 0} \right) & \; \\\begin{matrix}{K_{3} = {\rho_{AC} + \rho_{AD} - \rho_{BC} - \rho_{BD}}} \\{\approx {2\rho_{M}\sin\; 2{\delta_{M}\left( {{- \phi_{AC}} - \phi_{AD} + \phi_{BC} + \phi_{BD}} \right)}}} \\{= {4\rho_{M}\phi_{BA}\sin\; 2\delta_{M}}}\end{matrix} & (18) \\\begin{matrix}{K_{4} = {\rho_{AC} - \rho_{AD} + \rho_{BC} - \rho_{BD}}} \\{\approx {2\rho_{M}\sin\; 2{\delta_{M}\left( {{- \phi_{AC}} + \phi_{AD} - \phi_{BC} + \phi_{BD}} \right)}}} \\{= {4\rho_{M}\phi_{CD}\sin\; 2\delta_{M}}}\end{matrix} & (19)\end{matrix}$

K3 and K4 are not used to calculate angle shift, but may ratherrepresent additional degrees of freedom.

A basic estimate of angle shift may be derived from K2/K1≈sin 2δ_(M),so:

$\begin{matrix}{{\hat{\delta}}_{M\; 1} = {{\frac{1}{2}\sin^{- 1}\frac{K_{2}}{K_{1}}} \approx {\delta_{M}.}}} & (20)\end{matrix}$

Empirical analysis seeking to correlate the various residual errors withknown quantities, has shown that there are alternatives and improvementsto the preceding estimator {circumflex over (δ)}_(M1).

For example, suppose we have a quad matrix:

$M = \begin{bmatrix}M_{A\; C} & M_{AD} \\M_{BC} & M_{BD}\end{bmatrix}$where M_(ij) is some quantity relating source i to receiver j. (Examplesare the gains and transfer functions H_(ij)(T), K_(ij), and G_(ij)described above). Then define:

$M_{\chi} = \frac{M_{AD}M_{BC}}{M_{A\; C}M_{BD}}$as a ratio of the two possible pair-wise products between sources andreceivers. Thus:

$\begin{matrix}{{H_{\chi}(T)} = {\frac{{H_{AD}(T)}{H_{BC}(T)}}{{H_{A\; C}(T)}{H_{BD}(T)}}.}} & (21)\end{matrix}$

An empirical relation may be derived such that:

$\begin{matrix}{{\frac{1}{8}\ln\;{H_{\chi}(T)}} \approx {{\sin\left( {{\theta_{M}(T)} + \phi_{Q}} \right)} + {\frac{5}{6}{\sin^{3}\left( {{\theta_{M}(T)} + \phi_{Q}} \right)}} + {\frac{1}{8}{\sin^{2}\left( {\phi_{A\; C} - \phi_{BD}} \right)}} + {\frac{1}{8}{\sin^{2}\left( {\phi_{AD} - \phi_{BC}} \right)}} + {\frac{1}{8}\ln\; K\;\chi}}} & (22)\end{matrix}$where

$\begin{matrix}{K_{\chi} = \frac{K_{AD}K_{BC}}{K_{A\; C}K_{BD}}} & (23)\end{matrix}$

The empirical relation may relate the relative path-dependent gainswhich may be sensitive to reflection/refraction effects, and φ_(Q) (seeequation 1) may relate the common-mode positioning error between thesource/receiver polarizers (a change in φ_(Q) may not be able to bedistinguished from a polarization shift of the test medium). The sin²terms may be relatively small and may show dependence on thedifferential-mode positioning between the source and receive polarizers.The terms in equation 22 may be insensitive to changes insource/receiver gains and to any uniform attenuation that applies to allfour transfer paths. By subtracting the resultant quantities at time T₁from those at time T₀, the last three terms may cancel out and yield:

$\begin{matrix}\begin{matrix}{{\hat{S}}_{M\; 2} = {{\frac{1}{8}\ln\;{H_{\chi}\left( {T\; 1} \right)}} - {\frac{1}{8}\ln\;{H_{\chi}\left( {T\; 0} \right)}}}} \\{= {\frac{1}{8}\ln\frac{H_{\chi}\left( {T\; 1} \right)}{H_{\chi}\left( {T\; 0} \right)}}} \\{\approx {{\sin\left( {{\theta_{M}\left( {T\; 1} \right)} + \phi_{Q}} \right)} + {\frac{5}{6}{\sin^{3}\left( {{\theta_{M}\left( {T\; 1} \right)} + \phi_{Q}} \right)}} -}} \\{{\sin\left( {{\theta_{M}\left( {T\; 0} \right)} + \phi_{Q}} \right)} + {\frac{5}{6}{\sin^{3}\left( {{\theta_{M}\left( {T\; 0} \right)} + \phi_{Q}} \right)}}} \\{\approx {{\sin\;{\theta_{M}\left( {T\; 1} \right)}} - {\sin\;{\theta_{M}\left( {T\; 0} \right)}}}}\end{matrix} & (24)\end{matrix}$with estimators

$\begin{matrix}{{{\hat{\delta}}_{M\; 2} = {{\hat{S}}_{M\; 2} \approx \delta_{M}}}{{\hat{\delta}}_{M\; 2a} = {{\hat{S}}_{M\; 2}\left( {1 - {\frac{1}{6}{\hat{S}}_{M\; 2}^{2}}} \right)}}} & (25)\end{matrix}$where the estimator {circumflex over (δ)}_(M2a) may reduce errorslightly by compensating for the nonlinearity of equation 22, but notmuch when compared to unknown experimental sources of error (e.g.reflections or other nonlinearities).

The above estimators may be nearly equivalent to {circumflex over(δ)}_(M1) with similar accuracy and noise gain with respect to thetransfer function measurements (Hij).

Additionally, it may be possible to reduce the error further bycorrelating the residual error of these estimators with terms dependenton the common-mode polarizer misalignment φ_(Q), or the terms K3 and K4which may correlate with the differential modes of polarizermisalignment.

A third form of estimator has been derived empirically, and may bedefined as follows. Let

$\begin{matrix}{{H_{\gamma}(T)} = {\frac{{{H_{AD}(T)}{H_{BC}(T)}} - {{H_{A\; C}(T)}{H_{BD}(T)}}}{\begin{matrix}{{{H_{A\; C}(T)}{H_{AD}(T)}} + {{H_{A\; C}(T)}{H_{BC}(T)}} + {{H_{A\; C}(T)}H_{BD}(T)} +} \\{{{H_{AD}(T)}{H_{BD}(T)}} + {{H_{AD}(T)}{H_{BC}(T)}} + {{H_{BC}(T)}{H_{BD}(T)}}}\end{matrix}} = \frac{2\left( {{{H_{AD}(T)}{H_{BC}(T)}} - {{H_{A\; C}(T)}{H_{BD}(T)}}} \right)}{\begin{matrix}{\left( {{H_{A\; C}(T)} + {H_{AD}(T)} + {{H_{BC}(T)}{H_{BD}(T)}}} \right)^{2} -} \\{{H_{A\; C}^{2}(T)} - {H_{BD}^{2}(T)} - {H_{AD}^{2}(T)} - {H_{BC}^{2}(T)}}\end{matrix}}}} & (26)\end{matrix}$

This equation can be used to form an estimator using the followingequation:

$\begin{matrix}{{{\hat{S}}_{M\; 3} = {\frac{3}{4}\left( {{H_{\gamma}\left( {T\; 1} \right)} - {H_{\gamma}\left( {T\; 0}\; \right)}}\; \right)}}{{\hat{\delta}}_{M\; 3} = {{\hat{S}}_{M\; 3} \approx {\delta_{M}.}}}} & (27)\end{matrix}$

This may not be quite as accurate as {circumflex over (δ)}_(M1) and{circumflex over (δ)}_(M2a), as it may be sensitive to differences inthe source and receiver gains which may require compensation.

Consistent with the present disclosure, any suitable polarizer (such asa polarizing film) may be used for the first and second light sourcepolarizers and the first and second light receiver polarizers. Inaddition to conventional polarizers, in some embodiments, a Pockels cellmay be used, and in some embodiments, one or more liquid crystal display(LCD) units may be used as a polarizer. Liquid crystal displays maytypically use twisted nematic liquid crystals to control thepolarization angle shift in a liquid-crystal medium between 0° and 90°by application of an external voltage. The twisted nematic liquidcrystals may be sandwiched between two polarizers. The resulting systemmay allow the display to then either transmit or block light.

A similar arrangement may be used in connection with an embodiment ofquad matrix polarimeter, which may use a single light source and asingle light receiver. A light source and a light source polarizer maybe on one side of the test region. A light receiver polarizer and alight receiver may be on the other side of the test region. Atwisted-nematic cell (an LCD without polarizers) or other opticalrotator, that can be controlled to at least one of two polarizationrotation states (e.g., 0° and 90°), may be used as the light sourcepolarizer and/or the light receiver polarizer. The twisted-nematic celllight source polarizer and/or the twisted-nematic cell light receiverpolarizer may be oriented with their optical axes 45° apart.

Consistent with the above configuration, the effective relativepolarization of light between the light source polarizer and the lightreceiver polarizer may be θ_(M)±45°. Transfer functions H_(A) and H_(B)may be measured, one with the respective twisted-nematic cell polarizerat 0° and the other with the twisted-nematic cell polarizer at 90°. Thetwo measurements may be repeated twice, first at time T₀ and then attime T₁. Ratios ρ_(A)=H_(A)(T1)/H_(A)(T0) and ρ_(B)=H_(B)(T1)/H_(B)(T0)may be calculated. The change in polarization angle of a polarizingmedium in the test region between times T₀ and T₁ may

${be} \approx {\frac{1}{2}\sin^{- 1}\frac{\rho_{B} - \rho_{A}}{\rho_{B} + \rho_{A}}}$which may be shown through similar reasoning as that given above.

In a similar manner, a single polarizer may be used for light sourcepolarization and/or a single polarizer may be used for the lightreceiver polarizer. For example, the single polarizer may be rotated by90° to achieve the light source polarization axis shift and/or the lightreceiver polarization axis shift. Similarly, an optical merger/splitterpositioned between a single, stationary, polarizer and the test region(or between the light source and single polarizer or the singlepolarizer and the light receiver, on the other end of the test region)may be rotated to effect the polarization axis shift.

Further, one or more of the first light source polarizer and the secondlight source polarizer may include an interface surface disposed atBrewster's angle relative to an optical path between at least one of thefirst light source polarizer and the second light source polarizer andat least one of the first light receiver polarizer and the second lightreceiver polarizer. Similarly, one or more of the first light receiverpolarizer and the second light receiver polarizer may include aninterface surface disposed at Brewster's angle relative to an opticalpath between at least one of the first light source polarizer and thesecond light source polarizer and at least one of the first lightreceiver polarizer and the second light receiver polarizer. Referringalso to FIG. 4, Brewster's angle is the angle where reflected light (R1)and refracted light (R2) are at 90° relative to each other. Thereflected light (R1) may be polarized parallel to the plane ofreflection. The plane of reflection may be oriented to provide a desiredplane of polarization.

The relative angles at which a beam of incident light (I) is reflectedand refracted is dependent upon, at least in part, the refractiveindices of the two mediums at the interface. Accordingly, Brewster'sangle may be given by Θ_(B)=tan⁻¹(n₂/n₁), where n₁ is the refractiveindex of the first medium and n₂ is the refractive index of the secondmedium forming the interface.

Referring also to FIG. 5, an embodiment of quad matrix polarimeter 10 autilizing one or more at least partially reflective surfaces oriented atBrewster's angle as a light source polarizer (e.g., surface 12 a) and asa light receiver polarizer (e.g., surface 16 a) is diagrammaticallyshown. One embodiment of the apparatus is shown in FIG. 5A. In thisembodiment, the Brewster's angle polarizers are molded into the fluidpathway such that the polarized light does not need to pass throughanything other than the fluid under test. This embodiment may bedesirable for it eliminates the probability of the polarized light anglebeing shifted upon passing through a surface before passing through thefluid under test.

In some embodiments, surfaces 12 a, 16 a may be oriented at Brewster'sangle relative to the light path may allow light to be transmitted froma light source (e.g., light source 24) through one or more plasticcomponents (e.g., membrane m, which may randomly polarize the light dueto internal stresses in the plastic component), which may form at leasta portion of fluid passage 30, and be polarized upon reflection by atleast partially reflective surfaces 12 a, 16 a. As such, the randompolarizing effect of the one or more plastic components may not bedetrimental, and the need to provide a polarizer internal relative tothe one or more plastic components may be avoided.

Referring also to FIGS. 6 through 12, an exemplary embodiment of quadmatrix polarimeter 10 a is shown. As shown, quad matrix polarimeter 10 amay generally include at least partially reflective surfaces 12 a, 14 aoriented at Brewster's angle relative to an optical pathway throughfluid passage 30. Surfaces 12 a, 14 a may be oriented generallyperpendicular to one another, such that light (e.g., which may beprovided by light sources 24, 26) reflected from surfaces 12 a, 14 a maybe polarized with mutually perpendicular polarization axes. Similarly,quad matrix polarimeter 10 a may include at least partially reflectivesurfaces 16 a, 18 a at an opposed end of fluid passage 30. Surfaces 16a, 18 a may also be oriented at Brewster's angle relative to the opticalpathway through fluid passage 30. As shown, surfaces 16 a, 18 a may beoriented generally perpendicular to one another, such that light (e.g.,which may be transmitted from surfaces 12 a, 14 a) may be polarized withmutually perpendicular polarization axes. Additionally, surfaces 16 a,18 a may be generally oriented at +/−45 degrees relative to surfaces 12a, 14 a, such that the relative polarization angle of light transmittedfrom surfaces 12 a, 14 a and light transmitted from surfaces 16 a, 18 ato light receivers 20, 22 may be generally 45 degrees.

In one embodiment, surfaces 12 a, 14 a may be respective surfaces of anintegrally molded component (e.g., component 32). Component 32 mayinclude features 34, 36 for housing light sources 24, 26, respectively.Further, features 34, 36 may orient light sources 24, 26 in a desiredorientation relative to surfaces 12 a, 14 a. Similarly, in oneembodiment, surfaces 16 a, 18 a may be respective surfaces of anintegrally molded component (e.g., component 38). Component 38 mayinclude features 40, 42 for housing light receivers 20, 22. Further,features 34, 36 may orient light receivers 20, 22 in a desiredorientation relative to surfaces 16 a, 18 a.

While the description herein-above has generally related to an apparatusutilizing two light source polarizers and two light receiver polarizers,other implementations are contemplated herein. For example, lightsource/light receiver polarizers at relative angles of +45°, may workwell for small values of test medium polarization angle shift θ_(M). Ifthis angle is large, some of the approximations discussed above maybecome less accurate, and as θ_(M) approaches 45°, the ability to detectangle may become very poor because the transfer function curves may beat their minimum/maximum and have zero slope.

If it is desired to sense large polarization angles, one embodiment mayinclude the use of one of the following setups:

-   -   1. 2 sources approximately 45° apart, 3 receivers approximately        120° apart    -   2. 3 sources approximately 120° apart, 2 receivers approximately        45° apart    -   3. 3 sources approximately 120° apart, 3 receivers approximately        120° apart    -   4. 2 sources (A and B) approximately 45° apart, 2 receivers (C        and D) approximately 90° apart, with A and C approximately 90°        apart, and B and D approximately 45° apart.    -   5. The same as the previous setup but with sources and receivers        switched.

Each of the above alternatives may include the use of an appropriate setof optical mergers/splitters.

As will be discussed below, consistent the first two alternatives (twosources, three receivers or three sources, two receivers), having threesources or three receivers may allow the sensitivity to be good at allaxes. The third alternative (three sources and three receivers) may notbe necessary but may have some fault-tolerant advantages over the firsttwo. The fourth and fifth alternatives may ensure that there may be atleast two source-receiver transfer functions with nonzero slope

$\frac{\mathbb{d}H_{x}}{\mathbb{d}\;\theta_{m}},$but such a configuration may eliminate and/or reduce some of theself-compensating factors of the embodiment described above.

In an embodiment having three sources or three receivers, the sourcesmay be A and B and the receivers may be C, D, and E. Transfer functionsmay be derived that are generally similar and/or identical in form toequations 6 and 7, namely H_(ij)=G_(ij)(1+cos(2θ_(ij)+2θ_(m))) whereG_(ij) is a fixed constant that is a function of geometry/optics/signaland receiver strength and θ_(ij) is the relative optical axis anglebetween corresponding polarizers. As such, cos(2θ_(ij)+2θ_(m))=K_(c) cos2(θ_(m)+θ₀)−K_(s) sin 2(θ_(m)+θ₀) where θ₀ represents a fixed angleoffset between source A and receiver C that can be arbitrary, andK_(c)=cos 2(θ_(ij)−θ_(m)) and K_(s)=sin 2(θ_(ij)−θ_(m)).

i j (source) (receiver) θ_(ij) K_(c) K_(s) A C θ₀ 1 0 A D θ₀ + 120° −0.5−0.866 A E θ₀ + 240° −0.5 0.866 B C θ₀ + 45° 0 1 B D θ₀ + 165° 0.866−0.5 B E θ₀ + 285° −0.866 −0.5

The goal for a large-signal angle decoder for θ_(m) may be to achievetwo terms, one proportional to sin (2θ_(m)+2θ₀) and the other to cos(2θ_(m)+2θ₀), and then use a rectangular-to-polar conversion (or a4-quadrant arctangent) to compute the angle (2θ_(m)+2θ₀) from whichθ_(m) may be determined (within a given 180° sector). A slightmodification of the standard Clarke transform, as used in the field ofmotor control, may be used to convert the three receivers to two“virtual” receivers “x” and “y”, for instance:

$X_{Ax} = {{\frac{2}{3}X_{A\; C}} - {\frac{1}{3}X_{AD}} - {\frac{1}{3}X_{A\; E}}}$$X_{Bx} = {\frac{\sqrt{3}}{3}\left( {X_{BD} - X_{BE}} \right)}$$X_{Ay} = {\frac{\sqrt{3}}{3}\left( {X_{AE} - X_{AD}} \right)}$$X_{By} = {{\frac{2}{3}X_{BC}} - {\frac{1}{3}X_{BD}} - {\frac{1}{3}X_{BE}}}$

X_(Ax) and X_(Bx) may then be approximately proportional to sin(2θ_(m)+2θ₀) and X_(Ay) and X_(By) may be approximately proportional tosin (2θ_(m)+2θ₀). The “X”, in the exemplary embodiments, may be ageneric angle dependant function, or, in some embodiments, may be anygeneric quantity that may be roughly the optical transfer function,compensated for gain variation. This may be done either by calculatingX_(ij)=H_(ij)/G_(ij) where the system gain G_(ij) may be determined atmanufacturing time (but may be vulnerable to non-uniform gain driftsbetween sensor/receiver pairs), or X_(ij)=ρ_(ij)=H_(ij)(T₁)/H_(ij)(T₀).

The fact that there may be redundancy in the light receiver (fourtransfer functions sensitive to changes in one quantity, or six in thecase of some of the alternate embodiments) may mean that it may bepossible to take a measure of the “health” of the light receiver outputsto be used as an indication of light receiver failure. It mayadditionally be possible to compensate for any determined failure. Oneexample of a “health indicator” may be to use the quantities K₁ to K₄(see equations 16-19), e.g. examine quantity K₁ which may stay fairlyclose to 4ρ_(M), despite angle shifts, or to compute the followingempirically derived quantity:

$F_{341} = \frac{K_{3}^{2} + K_{4}^{2}}{K_{2}^{2} + a}$

The empirical number a may be used to prevent numerical overflow for K₂near 0 which may happen when θ_(m) is small. Indicator F₃₄₁ may remainsmall and fairly constant as it may be strongly correlated to therelative angular positions between various pairs of polarizers.

Consistent with the foregoing disclosure, there may be provided methodsand apparatus for facile measurement of the presence and/orconcentration of chiral molecules within a solution. Furthermore, thepresence and/or concentration of chiral molecules within a solution maybe determined in a non-invasive manner, which may reduce and/oreliminate the occurrence of contamination of the solution. As such, themethods and apparatus disclosed herein may find wide application withinboth medical fields of use and non-medical fields of use.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made. Accordingly, otherimplementations are within the scope of the following claims.

1. An apparatus comprising: a first polarized light source having afirst light source polarization axis; a second polarized light sourcehaving a second light source polarization axis generally perpendicularto the first light source polarization axis; a first polarized lightreceiver having a first polarized light receiver polarization axis andconfigured to measure an intensity of light transmitted from the firstlight receiver polarizer; and a second polarized light receiver having asecond polarized light receiver polarization axis substantiallyperpendicular to the first light receiver polarization axis andconfigured to measure an intensity of light transmitted from the secondlight receiver polarizer, wherein the first and second light receiverpolarization axes are generally +/−45 degrees relative to the first andsecond light source polarization axes.
 2. An apparatus comprising: afirst light source polarizer having a first light source polarizationaxis; a second light source polarizer having a second light sourcepolarization axis generally perpendicular to the first light sourcepolarization axis; a first light receiver polarizer having a first lightreceiver polarization axis; a first light receiver configured to measurean intensity of light transmitted from the first light receiverpolarizer; a second light receiver polarizer having a second lightreceiver polarization axis substantially perpendicular to the firstlight receiver polarization axis; and a second light receiver configuredto measure an intensity of light transmitted from the second lightreceiver polarizer; wherein the first and second light receiverpolarization axes are generally +/−45 degrees relative to the first andsecond light source polarization axes.
 3. The apparatus of claim 2,further comprising: a first light source configured to provide lightincident upon the first light source polarizer, the light incident uponthe first light source polarizer being substantially randomly polarized;and a second light source configured to provide light incident upon thesecond light source polarizer, the light incident upon the second lightsource polarizer being substantially randomly polarized.
 4. Theapparatus of claim 2, wherein one or more of the first light source andthe second light source include a laser diode.
 5. The apparatus of claim2, further including a test region, at least a portion of the testregion at least partially disposed between the first and second lightsource polarizers and the first and second light receiver polarizers. 6.The apparatus of claim 5, wherein the test region includes an at leastpartially transparent fluid passage configured to allow a fluidcontaining a concentration of chiral molecules to flow through the testregion.
 7. The apparatus of claim 6, wherein the chiral moleculesinclude glucose molecules.
 8. The apparatus of claim 2, wherein one ormore of the first light source polarizer and the second light sourcepolarizer comprise an interface surface disposed at Brewster's anglerelative to an optical path between at least one of the first lightsource polarizer and the second light source polarizer and at least oneof the first light receiver polarizer and the second light receiverpolarizer.
 9. The apparatus of claim 2, wherein one or more of the firstlight receiver polarizer and the second light receiver polarizercomprise an interface surface disposed at Brewster's angle relative toan optical path between at least one of the first light source polarizerand the second light source polarizer and at least one of the firstlight receiver polarizer and the second light receiver polarizer.
 10. Amethod comprising: receiving light via a first optical path including afirst light source polarizer having a first light source polarizationaxis and a first light receiver polarizer having a first light receiverpolarization axis being generally +45 degrees relative to the firstlight source polarization axis; receiving light via a second opticalpath including the first light source polarizer and a second lightreceiver polarizer having a second light receiver polarization axisbeing generally −45 degrees relative to the first light sourcepolarization axis; receiving light via a third optical path including asecond light source polarizer and the first light receiver polarizer,the second light source polarizer having a second light sourcepolarization axis being generally 90 degrees relative to the first lightsource polarization axis; and receiving light via a fourth optical pathincluding the second light source polarizer and the second lightreceiver polarizer.
 11. The method of claim 10, wherein receiving lightvia the first and the second optical paths includes directing light froma first light source incident upon the first light source polarizer, thelight from the first light source being substantially randomlypolarized.
 12. The method of claim 10, wherein receiving light via thethird and the fourth optical paths includes directing light from asecond light source incident upon the second light source polarizer, thelight from the second light source being substantially randomlypolarized.
 13. The method of claim 10, further including measuring anintensity of light received via the first and third optical paths by afirst light receiver, and measuring an intensity of light received viathe second and fourth optical paths by a second light receiver.
 14. Themethod of claim 13, wherein the first optical path, the second opticalpath, the third optical path, and the fourth optical path include a testregion, at least a portion of the test region being at least partiallydisposed between the first and second light source polarizers and thefirst and second light receiver polarizers.
 15. The method of claim 14,wherein the test region includes an at least partially transparent fluidpassage configured to allow a fluid containing a concentration of chiralmolecules to flow through the test region.
 16. The method of claim 15,further including determining a polarization angle shift associated withthe concentration of chiral molecules within the test region, basedupon, at least in part, the respective intensity of light received viathe first optical path, the second optical path, the third optical path,and the fourth optical path.
 17. The method of claim 10, wherein one ormore of the first light source polarizer and the second light sourcepolarizer comprise an interface surface disposed at Brewster's anglerelative to one or more of the first optical path, the second opticalpath, the third optical path, and the fourth optical path.
 18. Themethod of claim 10, wherein one or more of the first light receiverpolarizer and the second light receiver polarizer comprise an interfacesurface disposed at Brewster's angle relative to one or more of thefirst optical path, the second optical path, the third optical path, andthe fourth optical path.